I don't think anything would happen except lethargy and possible death from either one. Goldfish are coldwater and would probably get all lethargic in a hot betta tank and a betta would get all lethargic in a cold goldfish tank. Maybe the betta would get mad but I really don't know. Either way don't try that lol

Goldfish and bettas generally do not mix. The care requirements for both species are vastly different. Goldfish prefer cool, hard water with plenty of oxygenation, which usually means much more current. Bettas are tropical fish who do best in soft-neutral water with much gentler flow.

Your goldfish probably won't eat your betta but neither fish is going to be particularly happy in a joint set-up.

Goldfish are cold water fish.
Betta fish are tropical, and as such should never be kept in cold water unless you want a very lethargic, and possibly stressed (leading to sickness and/or death) betta fish.

I would never recommend having goldfish and betta fish together because they are completely different for environmental needs, and dietary needs as well. The goldfish also will grow to be a lot larger than what he is now, while the betta fish will probably barely grow anymore than he is already.

The size difference is the least of your problem - the amount of ammonia goldfish put out is scary, and in anything under 20-30 gallons can prove to be potentially lethal. Those with smaller tanks and goldfish usually have 60+ gallon filters, or double filters which then would irritate the betta fish.

Either way, they may or may not bug each other mainly because they would have to be dealing with stress, sickness and potential death

If you're referring Fancies, then they should work. Goldfish aren't pure cold water fish like Trout. Fancy Goldfish like mid 70s. I usually like to see what Olympia and koimaiden say in Goldfish threads. I learn quite a lot about Goldfish from them. ^.^

It's still an awful match, whether the same temperature. Goldfish need heavy filtration while bettas prefer still. Goldfish also get rather big and the betta can get eaten whether blind or not. And then the parameters... Basically what the other members said, but except the temperature part.

really the best way to have bettas and goldfish "together" would be with a large tank for the golds, and betta tanks on either side of their stand, that way they're not in the same tank, but in the same display.

i personally don't think it'd work aesthetically either, the color and shape just kinda clash (to me at least) so i'd use separate display setups, rather than display their tanks together.